Free energies for a rigid heat conductor with memory

The classical expressions of the free energy, introduced for viscoelastic solids, can be adapted to rigid heat conductors with memory, with a few changes. This includes an expression for the maximum free energy. For such materials, a free energy can also be given in terms of the minimal state descriptor, which corresponds to a new form recently derived for viscoelastic solids. Moreover, an expression for the internal dissipation associated which each of these free energies is derived. New forms of the free energy, with associated rates of dissipation, relating to the internal energy, are also derived.